1. **State the problem:** We have a right triangle with a right angle at vertex C. The side BC adjacent to angle B (70°) is 3 units, and we need to find the hypotenuse AC. 2. **Formula used:** In a right triangle, the cosine of an angle is the ratio of the adjacent side to the hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, $\theta = 70^\circ$, adjacent side $= BC = 3$, and hypotenuse $= AC$ (unknown). So, $$\cos(70^\circ) = \frac{3}{AC}$$ 4. **Solve for AC:** $$AC = \frac{3}{\cos(70^\circ)}$$ 5. **Calculate the value:** Using $\cos(70^\circ) \approx 0.3420$, $$AC = \frac{3}{0.3420} \approx 8.77$$ 6. **Final answer:** The length of the hypotenuse $AC$ is approximately **8.77** units.